Prepotentials for local mirror symmetry via Calabi-Yau fourfolds

In this paper, we first derive an intrinsic definition of classical triple intersection numbers of K_S, where S is a complex toric surface, and use this to compute the extended Picard-Fuchs system of K_S of our previous paper, without making use of the instanton expansion. We then extend this formalism to local fourfolds K_X, where X is a complex 3-fold. As a result, we are able to fix the prepotential of local Calabi-Yau threefolds K_S up to polynomial terms of degree 2. We then outline methods of extending the procedure to non canonical bundle cases.Comment: 42 pages, 7 figures. Expanded, reorganized, and added a theoretical background for the calculation

Density classification on infinite lattices and trees

Consider an infinite graph with nodes initially labeled by independent Bernoulli random variables of parameter p. We address the density classification problem, that is, we want to design a (probabilistic or deterministic) cellular automaton or a finite-range interacting particle system that evolves on this graph and decides whether p is smaller or larger than 1/2. Precisely, the trajectories should converge to the uniform configuration with only 0's if p1/2. We present solutions to that problem on the d-dimensional lattice, for any d>1, and on the regular infinite trees. For Z, we propose some candidates that we back up with numerical simulations

Contact process in a wedge

We prove that the supercritical one-dimensional contact process survives in certain wedge-like space-time regions, and that when it survives it couples with the unrestricted contact process started from its upper invariant measure. As an application we show that a type of weak coexistence is possible in the nearest-neighbor ``grass-bushes-trees'' successional model introduced in Durrett and Swindle (1991).Comment: 11 pages, 4 figure

1,3-Benzothia­zole–oxalic acid (2/1)

The asymmetric unit of the title compound, C7H5NS·0.5C2H2O4, contains one benzothia­zole mol­ecule and half an oxalic acid mol­ecule, the complete mol­ecule being generated by inversion symmetry. The benzothia­zole mol­ecule is essentially planar, with a maximum deviation of 0.007 (1) Å. In the crystal, the benzothia­zole mol­ecules inter­act with the oxalic acid mol­ecules via O—H⋯N and C—H⋯O hydrogen bonds generating R 2 2(8) (× 2) and R 4 4(10) motifs, thereby forming supra­molecular ribbons along [101]

A recent rebuilding of most spirals ?

Re-examination of the properties of distant galaxies leads to the evidence that most present-day spirals have built up half of their stellar masses during the last 8 Gyr, mostly during several intense phases of star formation during which they took the appearance of luminous infrared galaxies (LIRGs). Distant galaxy morphologies encompass all of the expected stages of galaxy merging, central core formation and disk growth, while their cores are much bluer than those of present-day bulges. We have tested a spiral rebuilding scenario, for which 75+/-25% of spirals have experienced their last major merger event less than 8 Gyr ago. It accounts for the simultaneous decreases, during that period, of the cosmic star formation density, of the merger rate, of the number densities of LIRGs and of compact galaxies, while the densities of ellipticals and large spirals are essentially unaffected.Comment: (1) GEPI, Obs. Meudon, France ;(2)Max-Planck Institut fuer Astronomie, Germany (3) National Astronomical Observatories, CAS, China. Five pages, 1 figure. To be published in "Starbursts: From 30 Doradus to Lyman Break Galaxies", held in Cambridge, ed. R. de Grijs & R. M. Gonzalez Delgado (Dordrecht: Kluwer

Multi-Channel Kondo Necklace

A multi--channel generalization of Doniach's Kondo necklace model is formulated, and its phase diagram studied in the mean--field approximation. Our intention is to introduce the possible simplest model which displays some of the features expected from the overscreened Kondo lattice. The $N$ conduction electron channels are represented by $N$ sets of pseudospins \vt_{j}, $j=1, ... , N$, which are all antiferromagnetically coupled to a periodic array of |\vs|=1/2 spins. Exploiting permutation symmetry in the channel index $j$ allows us to write down the self--consistency equation for general $N$. For $N>2$, we find that the critical temperature is rising with increasing Kondo interaction; we interpret this effect by pointing out that the Kondo coupling creates the composite pseudospin objects which undergo an ordering transition. The relevance of our findings to the underlying fermionic multi--channel problem is discussed.Comment: 29 pages (2 figures upon request from [email protected]), LATEX, submitted for publicatio

A Fermi Surface study of Ba1−x_{1-x}Kx_{x}BiO3_{3}

We present all electron computations of the 3D Fermi surfaces (FS's) in Ba$_{1-x}$K$_{x}$BiO$_{3}$ for a number of different compositions based on the selfconsistent Korringa-Kohn-Rostoker coherent-potential-approximation (KKR-CPA) approach for incorporating the effects of Ba/K substitution. By assuming a simple cubic structure throughout the composition range, the evolution of the nesting and other features of the FS of the underlying pristine phase is correlated with the onset of various structural transitions with K doping. A parameterized scheme for obtaining an accurate 3D map of the FS in Ba$_{1-x}$K$_{x}$BiO$_{3}$ for an arbitrary doping level is developed. We remark on the puzzling differences between the phase diagrams of Ba$_{1-x}$K$_{x}$BiO$_{3}$ and BaPb$_{x}$Bi$_{1-x}$O$_{3}$ by comparing aspects of their electronic structures and those of the end compounds BaBiO$_{3}$, KBiO$_3$ and BaPbO$_3$. Our theoretically predicted FS's in the cubic phase are relevant for analyzing high-resolution Compton scattering and positron-annihilation experiments sensitive to the electron momentum density, and are thus amenable to substantial experimental verification.Comment: 12 pages, 7 figures, to appear in Phys. Rev.

Topological (Sliced) Doping of a 3D Peierls System: Predicted Structure of Doped BaBiO3

At hole concentrations below x=0.4, Ba_(1-x)K_xBiO_3 is non-metallic. At x=0, pure BaBiO3 is a Peierls insulator. Very dilute holes create bipolaronic point defects in the Peierls order parameter. Here we find that the Rice-Sneddon version of Peierls theory predicts that more concentrated holes should form stacking faults (two-dimensional topological defects, called slices) in the Peierls order parameter. However, the long-range Coulomb interaction, left out of the Rice-Sneddon model, destabilizes slices in favor of point bipolarons at low concentrations, leaving a window near 30% doping where the sliced state is marginally stable.Comment: 6 pages with 5 embedded postscript figure